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¡@AnCAD Newsletter - Technical News
A Rectangular Plate With An Impact Force

    
National Center for Research on Earthquake Engineering, Taiwan
Dr. Vincent Yang

MATFOR is a set of libraries that enhance your code with visualization, shorten numerical code, and shorten development time.

The following example simulation includes MATFOR procedures in the source code for the graphical effects. This is a simulation of the dynamic behavior of a rectangular steel plate hit by an impact force. The plate is dimensioned with 1m-by-1m-by-5cm and is welded on a fixed wall on one side (see Fig. 1.) The impact force hits the plate at the opposite side of the welded surface.

Figure 1 : A rectangular plate hit by an impact force.

Finite element method is employed to simulate the dynamic response of the plate. In the tests, the plate is discretized into a structure mesh (see Fig. 2) using eight-noded incompatible solid element (Zienkiewicz and Taylor, 2000.) The ¡¥incompatible¡¦ solid element has several internal degrees-of-freedom representing bending shape functions, which is commonly believed to have higher quality (than a normal eight-noded solid element) on bending-dominated analysis cases. The Newmark¡¦s implicit dynamic analysis method is used for the dynamic time integration. The formulation of the eight-noded incompatible solid element and the Newmark¡¦s implicit analysis can be found in most of the finite element method textbook (e.g., Cook et al., 2002), and is not described here.

Figure 2 : Mesh discretization
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Figure 2-1 : Nonlinear dynamic analysis procedure. It shows the procedure of a nonlinear dynamic analysis procedure.

Figure 3 displays a sequence of the dynamic response of the plate after an impact force has been applied. After the force is applied, the shock wave begins to propagate over the plate. After a while the kinematic energy spreads throughout the plate which vibrates it in a relative low frequency. The contours in Fig. 3 represent the stress field along X axis at the bottom surface of the plate.

Figure 3 : Dynamic response of the plate

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